2.2 Extension theorem
Definition Pi system
- $(\Omega, \mathcal{F}, P)$,
- probability space
$P$ is said to be borrel probability measure if domain of $P$ is equal to $\mathcal{B}(\mathbb{R}^{n})$. We denote $\mathcal{B}(\mathbb{R}^{n})$ by borrel algebra.
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Definition Borrel probability measure
- $(\Omega, \mathcal{F}, P)$,
- probability space
$P$ is said to be borrel probability measure if domain of $P$ is equal to $\mathcal{B}(\mathbb{R}^{n})$. We denote $\mathcal{B}(\mathbb{R}^{n})$ by borrel algebra.
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Definition Regular measure
- $(\Omega, \mathcal{F}, P)$,
- probability space
$P$ is said to be regular masure if $P$ is a lebesgue extension of a borrel probability measure.
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